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A007892
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A Kutz sequence.
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2
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1, 4, 9, 1, 4, 9, 16, 4, 9, 16, 25, 9, 16, 25, 36, 16, 25, 36, 49, 25, 36, 49, 64, 36, 49, 64, 81, 49, 64, 81, 100, 64, 81, 100, 121, 81, 100, 121, 144, 100, 121, 144, 169, 121, 144, 169, 196, 144, 169, 196, 225, 169, 196, 225, 256, 196, 225, 256, 289, 225
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The pattern is obvious: after the initial three terms, we have four successive squares.
Another description of the same sequence: array read by rows, with four columns, in which row n lists n^2, (n+1)^2, (n+2)^2, n^2. - Omar E. Pol, Sep 28 2011
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REFERENCES
| R. E. Kutz, Two unusual sequences, Two-Year College Mathematics Journal, 12 (1981), 316-319.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,2,-2,0,0,-1,1).
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FORMULA
| a(n) = (floor((-1)^n+(n+5)/2)-3*floor((n+6)/4))^2. [Arkadiusz Wesolowski, Sep 27 2011]
a(n) = (n-3*floor(n/4))^2. [Arkadiusz Wesolowski, Sep 28 2011]
G.f.: x*(1+3*x+5*x^2-8*x^3+x^4-x^5-3*x^6+4*x^7)/((1-x)^3*(1+x+x^2+x^3)^2). a(n) = (A110657(n-1)+1)^2 = ((2*n-6*(-1)^((n-1)*n/2)-3*(-1)^n+9)/8)^2. [Bruno Berselli, Sep 28 2011]
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MATHEMATICA
| Table[(n - 3*Floor[n/4])^2, {n, 60}] (* Arkadiusz Wesolowski, Sep 29 2011 *)
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PROG
| (MAGMA) [(n-3*Floor(n/4))^2: n in [1..60]]; // Vincenzo Librandi, Sep 28 2011
(PARI) a(n)=(floor((-1)^n+(n+5)/2)-3*floor((n+6)/4))^2 \\ Charles R Greathouse IV, Sep 28 2011
(Maxima) makelist(((2*n-6*(-1)^((n-1)*n/2)-3*(-1)^n+9)/8)^2, n, 1, 60); [Bruno Berselli, Sep 28 2011]
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CROSSREFS
| Sequence in context: A011290 A196502 A129971 * A010297 A001191 A120865
Adjacent sequences: A007889 A007890 A007891 * A007893 A007894 A007895
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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